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In this paper, we introduce a data-driven modeling approach for dynamics problems with latent variables. The state-space of the proposed model includes artificial latent variables, in addition to observed variables that can be fitted to a…
A network of noisy bistable elements with global time-delayed couplings is considered. A dichotomous mean field model has recently been developed describing the collective dynamics in such systems with uniform time delays near the…
Most transportation networks are inherently temporal: Connections (e.g. flights, train runs) are only available at certain, scheduled times. When transporting passengers or commodities, this fact must be considered for the the planning of…
We study a dynamic traffic assignment model, where agents base their instantaneous routing decisions on real-time delay predictions. We formulate a mathematically concise model and define dynamic prediction equilibrium (DPE) in which no…
When making route decisions, travelers may engage in a certain degree of reasoning about what the others will do in the upcoming day, rendering yesterday's shortest routes less attractive. This phenomenon was manifested in a recent virtual…
Equilibrium is a rather ideal situation, the exception rather than the rule in Nature. Whenever the external or internal parameters of a physical system are varied its subsequent relaxation to equilibrium may be either impossible or take…
In this paper we consider the stability of a class of deterministic and stochastic SEIRS epidemic models with delay. Indeed, we assume that the transmission rate could be stochastic and the presence of a latency period of $r$ consecutive…
Robustness guarantees are important properties to be looked for during control design. They ensure stability of closed-loop systems in face of uncertainties, unmodeled effects and bounded disturbances. While the theory on robust stability…
People often deviate from expected utility theory when making risky and intertemporal choices. While the effects of probabilistic risk and time delay have been extensively studied in isolation, their interplay and underlying theoretical…
Long-term memory is a feature observed in systems ranging from neural networks to epidemiological models. The memory in such systems is usually modeled by the time delay. Furthermore, the nonlocal operators, such as the "fractional order…
Discrete breathers are ubiquitous structures in nonlinear anharmonic models ranging from the prototypical example of the Fermi-Pasta-Ulam model to Klein-Gordon nonlinear lattices, among many others. We propose a general criterion for the…
Linear dynamical systems are canonical models for learning-based control of plants with uncertain dynamics. The setting consists of a stochastic differential equation that captures the state evolution of the plant understudy, while the true…
When interpersonal interactions between individuals are described by the (discrete or continuous) dynamical systems, the interactions are usually assumed to be instantaneous: the rates of change of the actual states of the actors at given…
This paper is concerned with the study of the stability of dynamical systems evolving on time scales. We first {formalize the notion of matrix measures on time scales, prove some of their key properties and make use of this notion to study…
We find that the performance of state-of-the-art models on Natural Language Inference (NLI) and Reading Comprehension (RC) analysis/stress sets can be highly unstable. This raises three questions: (1) How will the instability affect the…
The same machine learning model running on different edge devices may produce highly-divergent outputs on a nearly-identical input. Possible reasons for the divergence include differences in the device sensors, the device's signal…
We address a class of Markov jump linear systems that are characterized by the underlying Markov process being time-inhomogeneous with a priori unknown transition probabilities. Necessary and sufficient conditions for uniform stochastic…
Numerical stability is of great significance for discrete-time dynamic vehicle model. Among the unstable factors, low-speed singularity stands out as one of the most challenging issues, which arises from that the denominator of tire side…
Stable matching is a fundamental problem studied both in economics and computer science. The task is to find a matching between two sides of agents that have preferences over who they want to be matched with. A matching is stable if no pair…
This paper provides a new unified framework for second-moment stability of discrete-time linear systems with stochastic dynamics. Relations of notions of second-moment stability are studied for the systems with general stochastic dynamics,…